Honors Geometry (2011-12)
Unit 9 Similarity– Test Review
Name:__________________
(Section 8-1, 8-2, 8-3, 8-5 and corresponding parts)
Hour:
____
For #1-5: Fill in the blank.
1)
If a line intersects a triangle such that it is __________________ to the third side of the triangle,
then the segments created on the two intersected sides of the triangle are proportional.
2)
Polygons are similar if and only if their angles are ___________ and corresponding sides are ____
3)
The 3 shortcuts for proving triangle similar are __________, _____________ and _____________
4)
A _______________________ is a mathematical statement that two fractions are equal.
5)
The ________________, _________________, and _______________________ of similar
triangles are proportional to the corresponding sides of the triangles.
For #6-9: Solve the following proportions for exact value unless specified otherwise.
6)
6 2
=
x 5
7)
8 4p
=
2
3
8)
5
3
=
x x +1
9)
round to nearest tenth
2x − 3 9 − x
=
7
8
For #10-13: Determine if the following figures are similar. If “YES,” find the similarity ratio and
make a similarity statement for the two figures.
10)
Similar?
YES
NO
11)
Similar?
YES
NO
Similarity Ratio: _____________
Similarity Ratio: _____________
_____________ ~ _____________
_____________ ~ _____________
12)
Similar?
YES
NO
13)
Similar?
YES
NO
Similarity Ratio: _____________
Similarity Ratio: _____________
_____________ ~ _____________
_____________ ~ _____________
For #14-22: The following figures are similar. Find the missing measures.
14)
x = __________
16)
x = __________
y ≈ __________
15)
Perimeter of NPQR = _____________
17)
x = __________
4.2
5
x
x
18)
4.5
x° = __________
z = __________
y = __________
19)
x = __________
2.7
20)
x = __________
y = __________
21)
x = __________
z = __________
22)
The figure is a blueprint of a house that is being designed. Determine the actual dimensions of the
following rooms.
7 ½ inches
a)
Library
5 inches
Playroom
b)
8 inches
Scale: 3 inches = 5 feet
23)
In a professional cooking class, there is a ratio 3 men to 10 women. If there are 221 people total at
the class, how many men are in the class?
# of Men = _________
24)
The Crocodile Hunter, Steve Irwin, wanted to measure the height of a giraffe on a sunny day. So,
he stood in the shadow of the giraffe and walked 8ft from the giraffe until the tip of his own
shadow is at the tip of the giraffe’s shadow. The tip of his own shadow is also 8 ft from him.
Steve is 6’ 3” tall. How tall is the giraffe? (Your answer must be in feet and inches without using
a decimal)
Height = ____________
25)
∆ABC ~ ∆DCE . D is a midpoint. Find EF and ED.
B
E
32
30
C
A
D
F
26)
AB ll DE. Write a proof to prove the triangles similar.
27) Find h.
B
A
B
A
17
60
17
60
C
C
21
h
D
h
D
30
21
30
E
E
28)
ABCDE ~ FGHIJ . Find the perimeter of both figures.
30)
Kite’s Area = 84 inches2
d1 = ______________
d1
31)
29) K ll l ll m ll n. Find w, x, y and z.
a ° = ________
b ° = ________
6 ft
32) A circle’s center is at (− 3,−1) and the end of a radius is at (− 10,23)
a)
Find the circumference of the circle
b)
Find the area of the circle.